Projet Classification
Margaux Bailleul et Oriane Duclos
2023-03-23
Chargement des librairies
library(corrplot)## corrplot 0.92 loadedlibrary(cluster)
library(NbClust)1 - Compréhension et pré-traitement des données
donnee <- read.csv("Pays_donnees.csv", sep = ',', row.names = 1)
head(donnee,5)## enfant_mort exports sant. imports revenu inflation
## Afghanistan 90.2 10.0 7.58 44.9 1610 9.44
## Albania 16.6 28.0 6.55 48.6 9930 4.49
## Algeria 27.3 38.4 4.17 31.4 12900 16.10
## Angola 119.0 62.3 2.85 42.9 5900 22.40
## Antigua and Barbuda 10.3 45.5 6.03 58.9 19100 1.44
## esper_vie fert pib_h
## Afghanistan 56.2 5.82 553
## Albania 76.3 1.65 4090
## Algeria 76.5 2.89 4460
## Angola 60.1 6.16 3530
## Antigua and Barbuda 76.8 2.13 12200str(donnee)## 'data.frame': 167 obs. of 9 variables:
## $ enfant_mort: num 90.2 16.6 27.3 119 10.3 14.5 18.1 4.8 4.3 39.2 ...
## $ exports : num 10 28 38.4 62.3 45.5 18.9 20.8 19.8 51.3 54.3 ...
## $ sant. : num 7.58 6.55 4.17 2.85 6.03 8.1 4.4 8.73 11 5.88 ...
## $ imports : num 44.9 48.6 31.4 42.9 58.9 16 45.3 20.9 47.8 20.7 ...
## $ revenu : int 1610 9930 12900 5900 19100 18700 6700 41400 43200 16000 ...
## $ inflation : num 9.44 4.49 16.1 22.4 1.44 20.9 7.77 1.16 0.873 13.8 ...
## $ esper_vie : num 56.2 76.3 76.5 60.1 76.8 75.8 73.3 82 80.5 69.1 ...
## $ fert : num 5.82 1.65 2.89 6.16 2.13 2.37 1.69 1.93 1.44 1.92 ...
## $ pib_h : int 553 4090 4460 3530 12200 10300 3220 51900 46900 5840 ...dim(donnee)## [1] 167 9Nous avons 167 individus et 9 variables
Statistiques descriptives
summary(donnee)## enfant_mort exports sant. imports
## Min. : 2.60 Min. : 0.109 Min. : 1.810 Min. : 0.0659
## 1st Qu.: 8.25 1st Qu.: 23.800 1st Qu.: 4.920 1st Qu.: 30.2000
## Median : 19.30 Median : 35.000 Median : 6.320 Median : 43.3000
## Mean : 38.27 Mean : 41.109 Mean : 6.816 Mean : 46.8902
## 3rd Qu.: 62.10 3rd Qu.: 51.350 3rd Qu.: 8.600 3rd Qu.: 58.7500
## Max. :208.00 Max. :200.000 Max. :17.900 Max. :174.0000
## revenu inflation esper_vie fert
## Min. : 609 Min. : -4.210 Min. :32.10 Min. :1.150
## 1st Qu.: 3355 1st Qu.: 1.810 1st Qu.:65.30 1st Qu.:1.795
## Median : 9960 Median : 5.390 Median :73.10 Median :2.410
## Mean : 17145 Mean : 7.782 Mean :70.56 Mean :2.948
## 3rd Qu.: 22800 3rd Qu.: 10.750 3rd Qu.:76.80 3rd Qu.:3.880
## Max. :125000 Max. :104.000 Max. :82.80 Max. :7.490
## pib_h
## Min. : 231
## 1st Qu.: 1330
## Median : 4660
## Mean : 12964
## 3rd Qu.: 14050
## Max. :105000# Histogramme de chaque variable
par(mfrow=c(3,3)) # Afficher les 9 histogrammes dans une grille 3x3
for (i in 1:9) {
hist(donnee[,i], main=colnames(donnee)[i], xlab="")
}
Pre-traimement
Donn ́ees manquantes ? Outliers
table(is.na(donnee))##
## FALSE
## 1503Aucune donnée manquante
Valeur aberrante exports max à 200 ? Bizarre Ce sont à première vue des pays riche comme malte, luxembourg, singapour import max à 174 ? Idem Finalement c’est logique Aucune valeur aberrante
Mais y a des valeurs “leviers”, certains pays comme malte, singapour se dégage des valeurs moyennes
Standardisation ?
Lorsque l’on a des données avec des unités différentes (par exemple des pourcentages, des espérances de vie, des PIB par habitant), il est recommandé de centrer et de réduire ces données. Centrer les données signifie soustraire la moyenne de la variable de toutes les observations, ce qui permet d’avoir une moyenne égale à zéro. Réduire les données signifie diviser chaque observation par l’écart-type de la variable, ce qui met toutes les variables à la même échelle. Cela facilite la comparaison entre les différentes variables et permet des analyses statistiques plus fiables. Il est cependant important de garder à l’esprit que la signification des résultats dépend toujours du contexte et de la validité des données utilisées
donnee <- data.frame(scale(donnee))Choix des variables (regroupement ?) en vue d’une classification
Matrice de corrélation
var <- donnee[,1:9]
corrplot(cor(var), type = "upper")
La matrice de corrélation nous aide à mieux comprendre les relations entre chaque variable et pourra nous aider à interpréter plus tard.
2 - Classification des pays en utilisant les différents algorithmes abordés en cours
Utilisation des algorithmes de classification vus en cours . Ŕeflexion sur les choix op ́er ́es D ́ecider d’une classification finale . Nombre de groupes ?
Partie 1 : Algoritlme des Kmeans
Tout d’abord nous allons utiliser l’algorithme des k-means pour avoir une première idée de notre classification finale. Si on ne sait pas a priori combien de groupes comporte le jeu de donnees, on peut appliquer l’algorithme pour plusieurs choix de K possibles et tracer la courbe d’évolution de l’inertie . On lance l’algorithme des kmeans et on observe l’évolution de la variance intra-groupes en fonction du nombre de groupes. On rajoute également l’option « nstart =50 » pour stabiliser les résultats.
A la vue de ce graphique, on aurait tendance à choisir K= 3,4 ou 5 groupes en appliquant la méthode dite « du coude »
K=4
cl = kmeans(donnee,K,nstart=50)
gpe = cl$cluster
clusplot(donnee,gpe,labels=4,col.p=gpe)
La représentation en clusplot nous permet de voir qu’il y a 4 groupes qui se séparent plutôt bien sur les composante 1, 2, 3 et 4. (on le voit au travers des différents couleur sur le graphique).
Representation des groupes sur le premier plan factoriel
Partie 2 : CAH
set.seed(123)
d <- dist(donnee)
#d <- dist(e19, method = "manhattan")
#d <- dist(e19, method = "minkowski")
cah.ward <- hclust(d, method = "ward.D")
cah.min <- hclust(d, method = "single")
cah.max <- hclust(d, method = "complete")Dengrogrammes
plot(cah.ward, hang = -1, main = "Distance de Ward", ylab = " ")
plot(cah.min, hang = -1, main = "Distance du saut minimal", ylab = " ")
plot(cah.max, hang = -1, main = "Distance du saut maximal", ylab = " ")
On s’apercoit raipdement que c’est le critère de Ward qui correspond le
mieux à nos données. On voit déjà qu’on peut partitionner nos données en
3 ou 4 groupes
Fonction de perte
Pour rappel, on cherche à maximiser l’inertie inter-classe. En effet, nous avons pour objectif de créer des groupes d’individus se ressemblant fortement (inertie intra-classes faible) et tels que les groupes soient les plus distints possible (inertie inter-classes élevée). L’inertie inter-classe est logiquement maximale (égale à l’intertie totale) lorsqu’il y a autant de classes que d’individus. Nous cherchons dans le graphique ci-dessous un “coude” qui correspond à une rupture dans la courbe (moment où l’inertie inter augmente beaucoup).
plot(rev(cah.ward$height)[1:10], type = "b", main = "Distance de Ward")
plot(rev(cah.min$height)[1:10], type = "b", main = "Distance du saut minimal")
plot(rev(cah.max$height)[1:10], type = "b", main = "Distance du saut maximal")
Avec le critère de Ward, la trace de la perte d’inertie nous incite à choisir des partitions en 3 groupes (“coude” très visible).
as.matrix(donnee)## enfant_mort exports sant.
## Afghanistan 1.28765971 -1.1348666486 0.278251399
## Albania -0.53733286 -0.4782201668 -0.096725279
## Algeria -0.27201464 -0.0988244217 -0.963176244
## Angola 2.00178723 0.7730561847 -1.443728879
## Antigua and Barbuda -0.69354825 0.1601861350 -0.286033893
## Argentina -0.58940465 -0.8101914437 0.467560013
## Armenia -0.50013871 -0.7408787595 -0.879443587
## Australia -0.82992677 -0.7773591196 0.696914681
## Austria -0.84232482 0.3717722236 1.523319592
## Azerbaijan 0.02305888 0.4812133039 -0.340642147
## Bahamas -0.60676192 -0.2228576461 0.391108458
## Bahrain -0.73570161 1.0357147775 -0.671932222
## Bangladesh 0.27597905 -0.9159844880 -1.199812011
## Barbados -0.59684348 -0.0586960256 0.420232860
## Belarus -0.81256951 0.3754202596 -0.438937004
## Belgium -0.83736560 1.2874292622 1.414103084
## Belize -0.48278145 0.6234867083 -0.588199565
## Benin 1.80341848 -0.6314376792 -0.988660095
## Bhutan 0.10984521 0.0507450547 -0.588199565
## Bolivia 0.20654998 0.0033205866 -0.719259375
## Bosnia and Herzegovina -0.77785497 -0.4162035546 1.559725095
## Botswana 0.35284694 0.0908734508 0.540371019
## Brazil -0.45798535 -1.1093303966 0.798850088
## Brunei -0.68858903 0.9591060212 -1.447369430
## Bulgaria -0.68115020 0.3316438275 0.019772330
## Burkina Faso 1.92739895 -0.7992473357 -0.027554824
## Burundi 1.37196643 -1.1742654376 1.741752609
## Cambodia 0.15199858 0.4739172319 -0.413453152
## Cameroon 1.72903019 -0.6898062554 -0.613683417
## Canada -0.81008990 -0.4380917707 1.632536100
## Cape Verde -0.29185152 -0.3067624743 -0.992300646
## Central African Republic 2.74567007 -1.0692020005 -1.032346699
## Chad 2.77046617 -0.1571929979 -0.832116434
## Chile -0.73322200 -0.1243606738 0.416592310
## China -0.55964934 -0.5402367790 -0.635526719
## Colombia -0.48774067 -0.9196325240 0.281891950
## Comoros 1.23806752 -0.8977443080 -0.839397534
## Congo Dem. Rep. 1.92739895 -0.0003274495 0.398389558
## Congo Rep. 0.63552242 1.6048083951 -1.585710340
## Costa Rica -0.69602786 -0.2885222943 1.486914090
## Cote d'Ivoire 1.80341848 0.3462359715 -0.551794063
## Croatia -0.81256951 -0.1280087098 0.343781304
## Cyprus -0.85968208 0.3316438275 -0.307877195
## Czech Republic -0.86464130 0.9080335171 0.387467907
## Denmark -0.84728404 0.3425879355 1.668941603
## Dominican Republic -0.09596237 -0.6715660753 -0.216863438
## Ecuador -0.32656605 -0.4818682028 0.452997812
## Egypt -0.22738167 -0.7226385795 -0.784789280
## El Salvador -0.47286301 -0.5183485629 0.034334531
## Equatorial Guinea 1.80341848 1.6303446471 -0.850319185
## Eritrea 0.41979640 -1.3249293248 -1.512899335
## Estonia -0.83736560 1.2400047940 -0.286033893
## Fiji -0.35136215 0.6088945643 -0.711978275
## Finland -0.87455974 -0.0878803137 0.777006786
## France -0.84480443 -0.5219965989 1.850969117
## Gabon 0.63056320 0.6052465282 -1.207093112
## Gambia 1.04217837 -0.6314376792 -0.409812602
## Georgia -0.53981246 -0.2228576461 1.195670068
## Germany -0.84480443 0.0434489827 1.741752609
## Ghana 0.90332024 -0.4234996266 -0.580918465
## Greece -0.85224326 -0.6934542914 1.268481073
## Grenada -0.58692504 -0.6314376792 -0.347923248
## Guatemala -0.07116628 -0.5584769590 0.012491229
## Guinea 1.75382629 -0.3943153386 -0.686494423
## Guinea-Bissau 1.87780676 -0.9561128841 0.613182024
## Guyana -0.01661487 0.3754202596 -0.522669661
## Haiti 4.20863965 -0.9415207401 0.034334531
## Hungary -0.80017146 1.4844232067 0.187237642
## Iceland -0.88447818 0.4483809798 0.940831549
## India 0.50906234 -0.6752141114 -1.006862847
## Indonesia -0.12323808 -0.6131974992 -1.531102086
## Iran -0.47038340 -0.6095494632 -0.442577555
## Iraq -0.03397213 -0.0623440616 0.580417072
## Ireland -0.84480443 2.2578068409 0.864379993
## Israel -0.83488599 -0.2228576461 0.296454151
## Italy -0.84976365 -0.5803651751 0.988158702
## Jamaica -0.50013871 -0.3578349785 -0.730181026
## Japan -0.86960052 -0.9524648481 0.973596501
## Jordan -0.42575043 0.2623311433 0.445716712
## Kazakhstan -0.41583199 0.1127616669 -0.919489640
## Kenya 0.59336906 -0.7445267956 -0.752024328
## Kiribati 0.60576711 -1.0144814603 1.632536100
## Kuwait -0.68115020 0.9335697692 -1.523820985
## Kyrgyz Republic -0.21498363 0.3827163316 -0.231425639
## Lao 1.00746384 -0.2082655020 -0.853959735
## Latvia -0.75553849 0.4593250878 -0.049398125
## Lebanon -0.69354825 -0.1936733580 0.078021134
## Lesotho 1.52322261 -0.0623440616 1.559725095
## Liberia 1.26534322 -0.8028953717 1.814563614
## Libya -0.53733286 0.8934413731 -1.068752201
## Lithuania -0.79769185 0.8824972650 0.081661685
## Luxembourg -0.87951896 4.8843927683 0.347421854
## Macedonia FYR -0.69106864 -0.0477519176 0.099864436
## Madagascar 0.59336906 -0.5876612471 -1.108798254
## Malawi 1.29509854 -0.6679180393 -0.082163078
## Malaysia -0.75305888 1.6704730432 -0.883084138
## Maldives -0.62163958 1.3312056943 -0.176817385
## Mali 2.44811694 -0.6679180393 -0.668291671
## Malta -0.78033458 4.0818248460 0.667790278
## Mauritania 1.46619159 0.3498840075 -0.875803037
## Mauritius -0.57700661 0.3681241876 -0.296955544
## Micronesia Fed. Sts. 0.04289576 -0.6423817873 2.688295679
## Moldova -0.52245520 -0.0696401337 1.778158111
## Mongolia -0.30176996 0.2039625671 -0.500826359
## Montenegro -0.78033458 -0.1498969259 0.835255591
## Morocco -0.11827886 -0.3250026544 -0.588199565
## Mozambique 1.55545753 -0.3505389064 -0.584559015
## Myanmar 0.64792047 -1.4956938904 -1.764097303
## Namibia 0.43963327 0.2440909632 -0.012992623
## Nepal 0.21646842 -1.1501883999 -0.569996814
## Netherlands -0.83736560 1.1269156777 1.850969117
## New Zealand -0.79521224 -0.3943153386 1.195670068
## Niger 2.10097161 -0.6898062554 -0.602761767
## Nigeria 2.27454427 -0.5767171391 -0.635526719
## Norway -0.86960052 -0.0513999536 0.969955951
## Oman -0.65883372 0.8970894091 -1.472853282
## Pakistan 1.33477229 -1.0071853883 -1.680364647
## Panama -0.46046496 1.0539549575 0.467560013
## Paraguay -0.35136215 0.5103975920 -0.344282697
## Peru -0.44558730 -0.4855162388 -0.631886169
## Philippines -0.15795261 -0.2301537181 -1.167047059
## Poland -0.80017146 -0.0368078096 0.234564796
## Portugal -0.85224326 -0.4089074826 1.523319592
## Qatar -0.72578317 0.7730561847 -1.822346108
## Romania -0.66379294 -0.3104105103 -0.449858655
## Russia -0.70098708 -0.4344437347 -0.631886169
## Rwanda 0.62808359 -1.0619059284 1.341292079
## Samoa -0.48030184 -0.4344437347 -0.125849681
## Saudi Arabia -0.55964934 0.3097556114 -0.919489640
## Senegal 0.70743109 -0.5913092831 -0.420734253
## Serbia -0.76049771 -0.2994664023 1.304886576
## Seychelles -0.59188426 1.9221875279 -1.243498614
## Sierra Leone 3.01842711 -0.8868002000 2.287835149
## Singapore -0.87951896 5.7964017708 -1.039627799
## Slovak Republic -0.77537536 1.2837812262 0.718757982
## Slovenia -0.86960052 0.8460169049 0.944472099
## Solomon Islands -0.25217777 0.2988115034 0.631384776
## South Africa 0.38260226 -0.4563319507 0.773366236
## South Korea -0.84728404 0.3024595394 0.041615632
## Spain -0.85472287 -0.5694210671 0.991799253
## Sri Lanka -0.67123177 -0.7846551917 -1.410963927
## St. Vincent and the Grenadines -0.43566887 -0.5183485629 -0.853959735
## Sudan 0.95291243 -0.7810071557 -0.180457935
## Suriname -0.35136215 0.4155486557 0.070740034
## Sweden -0.87455974 0.1857223871 1.024564205
## Switzerland -0.83736560 0.8350727969 1.705347106
## Tajikistan 0.35036733 -0.9561128841 -0.304236644
## Tanzania 0.83389118 -0.8174875158 -0.293314993
## Thailand -0.57948622 0.9262736971 -1.068752201
## Timor-Leste 0.60328750 -1.4194134574 0.838896141
## Togo 1.29013932 -0.0331597736 0.303735251
## Tonga -0.51749598 -1.0473137844 -0.635526719
## Tunisia -0.51749598 0.3425879355 -0.220503988
## Turkey -0.47534262 -0.7554709036 -0.027554824
## Turkmenistan 0.58840984 1.2837812262 -1.571148139
## Uganda 1.05953564 -0.8758560919 0.798850088
## Ukraine -0.65883372 0.2185547112 0.329219103
## United Arab Emirates -0.73570161 1.3348537303 -1.148844307
## United Kingdom -0.82000833 -0.4709240948 1.028204755
## United States -0.76793653 -1.0473137844 4.035299280
## Uruguay -0.68610942 -0.5402367790 0.558573770
## Uzbekistan -0.04884979 -0.3432428344 -0.366125999
## Vanuatu -0.22490206 0.2003145311 -0.569996814
## Venezuela -0.52493481 -0.4599799868 -0.693775523
## Vietnam -0.37119902 1.1269156777 0.008850679
## Yemen 0.44707210 -0.4052594466 -0.595480666
## Zambia 1.11160744 -0.1498969259 -0.337001597
## imports revenu inflation
## Afghanistan -0.08220771 -0.805821873 0.156864451
## Albania 0.07062429 -0.374243349 -0.311410892
## Algeria -0.63983800 -0.220182266 0.786907640
## Angola -0.16481961 -0.583289197 1.382894441
## Antigua and Barbuda 0.49607554 0.101426731 -0.599944185
## Argentina -1.27594958 0.080677763 1.240992822
## Armenia -0.06568534 -0.541791262 -0.001119352
## Australia -1.07355044 1.258181668 -0.626432487
## Austria 0.03757953 1.351552022 -0.653582997
## Azerbaijan -1.08181163 -0.059377768 0.569325158
## Bahamas -0.13177485 0.298541922 -0.773347964
## Bahrain 0.16562797 1.242619943 -0.032337708
## Bangladesh -1.03637509 -0.762767766 -0.060718032
## Barbados 0.07475488 -0.095688461 -0.705802793
## Belarus 0.72738885 -0.049003284 0.692306561
## Belgium 1.14870951 1.242619943 -0.558319710
## Belize 0.43824722 -0.480581808 -0.628324509
## Benin -0.40026351 -0.794928665 -0.652447784
## Bhutan 0.98348572 -0.556315539 -0.169509273
## Bolivia -0.52005075 -0.608706682 0.094427739
## Bosnia and Herzegovina 0.18215035 -0.385136557 -0.603728228
## Botswana 0.18215035 -0.199433298 0.107671890
## Brazil -1.44943456 -0.137186396 0.059425339
## Brunei -0.78027822 3.291580483 0.843668288
## Bulgaria 0.25237046 -0.095688461 -0.631162541
## Burkina Faso -0.71418870 -0.815158909 -0.091936388
## Burundi -0.31765161 -0.849705939 0.427423538
## Cambodia 0.52085911 -0.758617972 -0.441014371
## Cameroon -0.82158417 -0.751355833 -0.555481677
## Canada -0.65636038 1.221870975 -0.464664641
## Cape Verde 0.61586279 -0.586920266 -0.688396194
## Central African Republic -0.84223714 -0.843273759 -0.546021570
## Chad -0.14003604 -0.789222699 -0.131668841
## Chile -0.64396859 0.116988456 0.111455933
## China -1.00333033 -0.394992317 -0.079638248
## Colombia -1.20159888 -0.323927103 -0.371009572
## Comoros 0.19867273 -0.816196357 -0.370063562
## Congo Dem. Rep. 0.11193024 -0.857746164 1.231532714
## Congo Rep. 0.32259057 -0.620118614 1.222072606
## Costa Rica -0.49113659 -0.214995024 -0.114640647
## Cote d'Ivoire -0.14829723 -0.749799661 -0.226269921
## Croatia -0.36308815 0.153299149 -0.658502253
## Cyprus 0.43824722 0.869138528 -0.546021570
## Czech Republic 0.66129933 0.578652983 -0.871449283
## Denmark -0.13590545 1.393049957 -0.431554263
## Dominican Republic -0.56135670 -0.313552619 -0.221539867
## Ecuador -0.59853205 -0.404329352 -0.029499676
## Egypt -0.83810654 -0.377874419 0.219301164
## El Salvador -0.01198760 -0.510667811 -0.485476879
## Equatorial Guinea 0.49607554 0.858764044 1.619397140
## Eritrea -0.97441617 -0.815677633 0.361202783
## Estonia 0.90087383 0.288167438 -0.571563861
## Fiji 0.70260528 -0.508074190 -0.336007173
## Finland -0.39200232 1.175185798 -0.702964760
## France -0.77614762 1.024755784 -0.636838606
## Gabon -1.15616234 -0.090501219 0.834208180
## Gambia -0.17308080 -0.803228252 -0.329385098
## Georgia 0.24410927 -0.540235089 0.072669490
## Germany -0.40439410 1.206309250 -0.664462121
## Ghana -0.04090177 -0.730606866 0.834208180
## Greece -0.66875216 0.599401950 -0.672503213
## Grenada 0.09540786 -0.308365377 -0.690761221
## Guatemala -0.43743886 -0.541272538 -0.249920191
## Guinea -0.15242782 -0.827608289 0.786907640
## Guinea-Bissau -0.48287540 -0.817233805 -0.455204533
## Guyana 1.33045567 -0.586401542 -0.194105554
## Haiti 0.73565004 -0.811527839 -0.220593856
## Hungary 1.22306021 0.267418470 -0.515749224
## Iceland -0.14829723 1.123313380 -0.218701835
## India -0.81745357 -0.660579101 0.113347954
## Indonesia -1.01159152 -0.452051977 0.711226777
## Iran -1.13550936 0.013243619 0.767987425
## Iraq -0.52831194 -0.230556749 0.834208180
## Ireland 1.63611968 1.481233069 -1.040785215
## Israel -0.57787908 0.646087127 -0.568725829
## Italy -0.81332298 0.988445091 -0.705991995
## Jamaica 0.11193024 -0.474357117 0.191866850
## Japan -1.37508386 0.967696123 -0.915911790
## Jordan 0.91326561 -0.398104662 0.061317361
## Kazakhstan -0.70179692 0.153299149 1.108551311
## Kenya -0.54896492 -0.760692869 -0.538453483
## Kiribati 1.36350043 -0.799597183 -0.592376098
## Kuwait -0.68114395 3.011469422 0.323362351
## Kyrgyz Republic 1.43785114 -0.744612419 0.209841056
## Lao 0.09953845 -0.682884241 0.134160192
## Latvia 0.33911295 0.059928796 -0.812985816
## Lebanon 0.54977328 -0.043816042 -0.713654682
## Lesotho 2.23505591 -0.765880111 -0.343575259
## Liberia 1.88808596 -0.853025774 -0.218701835
## Libya -0.19786437 0.646087127 0.607165589
## Lithuania 0.83891490 0.205171568 -0.511019170
## Luxembourg 3.92859974 3.867364331 -0.393713832
## Macedonia FYR 0.46303079 -0.297990894 -0.543183537
## Madagascar -0.16068901 -0.817233805 0.095373749
## Malawi -0.49526718 -0.835907876 0.408503322
## Malaysia 0.99587750 0.205171568 -0.048419891
## Maldives 0.76456420 -0.344676071 -0.463718630
## Mali -0.48700600 -0.792335044 -0.322763022
## Malta 4.42427111 0.578652983 -0.373847605
## Mauritania 0.59107922 -0.717120037 1.051790663
## Mauritius 0.63238517 -0.064565009 -0.629270519
## Micronesia Fed. Sts. 1.40893697 -0.716082589 -0.376685637
## Moldova 1.30567211 -0.686515310 0.313902243
## Mongolia 0.40520246 -0.489400119 2.972192577
## Montenegro 0.65303814 -0.163122605 -0.584808012
## Morocco -0.16068901 -0.555278091 -0.643839086
## Mozambique -0.02850998 -0.841717587 -0.013417492
## Myanmar -1.93412267 -0.696371070 -0.070178140
## Namibia 0.57042625 -0.450495805 -0.399389896
## Nepal -0.43330826 -0.786110354 0.692306561
## Netherlands 0.69021350 1.470858585 -0.655948024
## New Zealand -0.78027822 0.786142658 -0.383307713
## Niger 0.09127726 -0.847112318 -0.494936987
## Nigeria -1.21812126 -0.622193511 9.102342527
## Norway -0.75962525 2.342315220 -0.173293316
## Oman -0.23503972 1.460484101 0.739607101
## Pakistan -1.13550936 -0.667322515 0.294982027
## Panama 1.29328032 -0.090501219 -0.491152943
## Paraguay 0.19041154 -0.511186535 -0.159103154
## Peru -0.95376320 -0.372687177 -0.195997575
## Philippines -0.42504707 -0.598850922 -0.336953184
## Poland -0.19786437 0.241482261 -0.579131947
## Portugal -0.39200232 0.521593322 -0.675341245
## Qatar -0.95376320 5.594715874 -0.075854204
## Romania -0.33417399 0.033992586 -0.402227929
## Russia -1.06528925 0.308916405 0.607165589
## Rwanda -0.69766632 -0.819308702 -0.489260922
## Samoa 0.25650105 -0.609225406 -0.573455883
## Saudi Arabia -0.57374848 1.465671343 0.890968828
## Senegal -0.27221507 -0.776254594 -0.561157742
## Serbia 0.04171013 -0.230556749 -0.179915392
## Seychelles 2.52419754 0.168860875 -1.134440284
## Sierra Leone -0.51178956 -0.826052116 0.890968828
## Singapore 5.25039005 2.850664923 -0.740521389
## Slovak Republic 1.27675794 0.417848485 -0.690288216
## Slovenia 0.66129933 0.599401950 -0.829541005
## Solomon Islands 1.41719816 -0.797003562 -0.091936388
## South Africa -0.80506179 -0.266867442 -0.135452885
## South Korea -0.02850998 0.687585062 -0.437230328
## Spain -0.82984536 0.796517142 -0.721033567
## Sri Lanka -0.82984536 -0.445308563 1.420734873
## St. Vincent and the Grenadines 0.42172484 -0.374762073 -0.316140946
## Sudan -1.22638245 -0.714526416 1.118011419
## Suriname -0.35069637 -0.152748121 -0.055041967
## Sweden -0.25569269 1.335990296 -0.642420070
## Switzerland 0.26476224 1.989582772 -0.706181197
## Tajikistan 0.48368376 -0.779885664 0.446343754
## Tanzania -0.73484168 -0.780923112 0.138890246
## Thailand 0.57455684 -0.189058814 -0.350197335
## Timor-Leste -0.78853941 -0.793372493 1.770758867
## Togo 0.42998603 -0.826570841 -0.624540466
## Tonga 0.55390387 -0.631011822 -0.388037767
## Tunisia 0.34737414 -0.349863312 -0.374793616
## Turkey -0.88354309 0.044367070 -0.073016172
## Turkmenistan -0.09873009 -0.373724625 -0.517641246
## Uganda -0.75549465 -0.809452942 0.266601703
## Ukraine 0.17388916 -0.483694153 0.531484726
## United Arab Emirates 0.69021350 2.098514852 0.446343754
## United Kingdom -0.66462157 0.988445091 -0.587646045
## United States -1.28421077 1.673161018 -0.620756422
## Uruguay -0.88767368 -0.002318107 -0.271678439
## Uzbekistan -0.75962525 -0.669397412 0.824748072
## Vanuatu 0.23997867 -0.736312832 -0.488314911
## Venezuela -1.20986007 -0.033441558 3.606019809
## Vietnam 1.37589222 -0.656429307 0.408503322
## Yemen -0.51592016 -0.656948031 1.496415737
## Zambia -0.66049097 -0.719194934 0.588245374
## esper_vie fert pib_h
## Afghanistan -1.614237166 1.897176463 -0.677143083
## Albania 0.645923798 -0.857394179 -0.484167091
## Algeria 0.668412962 -0.038289240 -0.463980176
## Angola -1.175698472 2.121769753 -0.514720259
## Antigua and Barbuda 0.702146708 -0.540321300 -0.041691745
## Argentina 0.589700889 -0.381784860 -0.145354280
## Armenia 0.308586341 -0.830971439 -0.531633620
## Australia 1.286864967 -0.672434999 2.124309640
## Austria 1.118196239 -0.996113564 1.851513496
## Azerbaijan -0.163686100 -0.679040684 -0.388688441
## Bahamas 0.364809250 -0.718674794 0.820344071
## Bahrain 0.612190052 -0.520504245 0.422061700
## Bangladesh -0.017506535 -0.408207600 -0.665958441
## Barbados 0.690902126 -0.771520274 0.165633325
## Belarus -0.017506535 -0.963085139 -0.378322187
## Belgium 1.061973329 -0.718674794 1.715115424
## Belize 0.094939284 -0.157191570 -0.470527284
## Benin -0.984540579 1.593314954 -0.665958441
## Bhutan 0.173651358 -0.375179175 -0.588375218
## Bolivia 0.117428448 0.166486995 -0.599287064
## Bosnia and Herzegovina 0.702146708 -1.081987469 -0.455796292
## Botswana -1.513035929 -0.044894925 -0.360863234
## Brazil 0.409787578 -0.758308904 -0.096250974
## Brunei 0.735880453 -0.731886164 1.218626441
## Bulgaria 0.376053832 -0.910239659 -0.334129212
## Burkina Faso -1.423079274 1.930204888 -0.675942780
## Burundi -1.445568438 2.187826603 -0.694711155
## Cambodia -0.501023557 -0.044894925 -0.664430783
## Cameroon -1.490546765 1.428172829 -0.635841747
## Canada 1.208152894 -0.870605549 1.878793110
## Cape Verde 0.218629685 -0.183614310 -0.526723289
## Central African Republic -2.592515793 1.494229679 -0.682980921
## Chad -1.580503421 2.405814208 -0.658374709
## Chile 0.960772092 -0.705463424 -0.003500285
## China 0.454765906 -0.897028289 -0.458524253
## Colombia 0.657168380 -0.619589519 -0.366319157
## Comoros -0.523512721 1.190368169 -0.665358290
## Congo Dem. Rep. -1.468057602 2.372785783 -0.689091555
## Congo Rep. -1.141964726 1.322481869 -0.557822050
## Costa Rica 1.106951657 -0.679040684 -0.259928660
## Cote d'Ivoire -1.602992585 1.533863789 -0.640752078
## Croatia 0.645923798 -0.923451029 0.029235252
## Cyprus 1.050728747 -1.009324934 0.973109911
## Czech Republic 0.780858781 -0.949873769 0.372958394
## Denmark 1.005750419 -0.712069109 2.457120936
## Dominican Republic 0.454765906 -0.229854105 -0.409966540
## Ecuador 0.690902126 -0.190219995 -0.453068331
## Egypt -0.006261953 0.159881310 -0.565460342
## El Salvador 0.398542996 -0.447841710 -0.544182243
## Equatorial Guinea -1.085741816 1.494229679 0.225648476
## Eritrea -0.995785161 1.097888579 -0.681016789
## Estonia 0.612190052 -0.811154384 0.089250404
## Fiji -0.590980212 -0.183614310 -0.508173152
## Finland 1.061973329 -0.712069109 1.813322035
## France 1.219397476 -0.606378149 1.507790354
## Gabon -0.860850178 0.747787274 -0.229921085
## Gambia -0.568491048 1.824513928 -0.676652050
## Georgia 0.252363431 -0.679040684 -0.545819020
## Germany 1.073217911 -1.029141989 1.573261429
## Ghana -0.939562252 0.873295289 -0.635841747
## Greece 1.106951657 -0.969690824 0.760328919
## Grenada 0.083694703 -0.467658765 -0.305212820
## Guatemala 0.083694703 0.285389325 -0.552911719
## Guinea -1.411834692 1.580103584 -0.671959957
## Guinea-Bissau -1.681704658 1.388538719 -0.677470439
## Guyana -0.568491048 -0.196825680 -0.541454281
## Haiti -4.324181408 0.252360900 -0.671196127
## Hungary 0.443521324 -1.121621579 0.007411561
## Iceland 1.286864967 -0.494081505 1.578717351
## India -0.489778975 -0.229854105 -0.633659378
## Indonesia -0.073729444 -0.309122325 -0.537635135
## Iran 0.443521324 -0.784731644 -0.351042573
## Iraq -0.377333156 1.064860154 -0.461797807
## Ireland 1.106951657 -0.593166779 1.949720108
## Israel 1.219397476 0.054190350 0.962198066
## Italy 1.253131222 -0.982902194 1.245906056
## Jamaica 0.466010488 -0.513898560 -0.451977146
## Japan 1.376821623 -1.029141989 1.720571346
## Jordan 0.589700889 0.470348505 -0.506536375
## Kazakhstan -0.242398173 -0.229854105 -0.212462131
## Kenya -0.872094760 0.939352139 -0.654555563
## Kiribati -1.108230980 0.589250834 -0.626021086
## Kuwait 0.859570855 -0.487475820 1.393215973
## Kyrgyz Republic -0.231153591 0.100430145 -0.659302216
## Lao -0.759648941 0.133458570 -0.645116816
## Latvia 0.286097177 -1.048959044 -0.090795051
## Lebanon 1.039484165 -0.883816919 -0.223919569
## Lesotho -2.704961612 0.232543845 -0.643480039
## Liberia -1.096986398 1.368721664 -0.689473469
## Libya 0.623434634 -0.355362120 -0.047147668
## Lithuania 0.297341759 -0.956479454 -0.052603591
## Luxembourg 1.208152894 -0.870605549 5.021404691
## Macedonia FYR 0.387298414 -0.976296509 -0.459615438
## Madagascar -1.096986398 1.091282894 -0.684781375
## Malawi -1.962819206 1.560286529 -0.682271651
## Malaysia 0.443521324 -0.527109930 -0.212462131
## Maldives 0.825837109 -0.474264450 -0.319943812
## Mali -1.243165963 2.379391468 -0.668686403
## Malta 1.095707075 -1.048959044 0.443885392
## Mauritania -0.264887337 1.342298924 -0.641843262
## Mauritius 0.319830923 -0.910239659 -0.270840506
## Micronesia Fed. Sts. -0.579735630 0.338234805 -0.551274942
## Moldova -0.096218608 -1.108410209 -0.618382794
## Mongolia -0.489778975 -0.203431365 -0.562732381
## Montenegro 0.657168380 -0.778125959 -0.342858688
## Morocco 0.331075505 -0.243065475 -0.552911719
## Mozambique -1.805395059 1.725428653 -0.684454020
## Myanmar -0.422311484 -0.355362120 -0.653409819
## Namibia -1.344367201 0.430714395 -0.424151939
## Nepal -0.253642755 -0.223248420 -0.675015273
## Netherlands 1.140685402 -0.764914589 2.037014874
## New Zealand 1.163174566 -0.513898560 1.131331675
## Niger -1.321878037 3.000325857 -0.688327725
## Nigeria -1.130720144 1.910387833 -0.580191334
## Norway 1.174419148 -0.659223629 4.082985955
## Oman 0.623434634 -0.031683555 0.345678780
## Pakistan -0.590980212 0.595856519 -0.650572739
## Panama 0.814592527 -0.216642735 -0.266475768
## Paraguay 0.398542996 -0.143980200 -0.531088028
## Peru 0.825837109 -0.269488215 -0.433427008
## Philippines -0.174930682 0.140064255 -0.591103180
## Poland 0.645923798 -1.015930619 -0.019868054
## Portugal 1.039484165 -1.029141989 0.520268312
## Qatar 1.005750419 -0.579955409 3.128199451
## Romania 0.353564668 -0.897028289 -0.258291884
## Russia -0.152441518 -0.910239659 -0.123530588
## Rwanda -0.669692286 1.031831729 -0.676597491
## Samoa 0.106183866 0.919535084 -0.519084997
## Saudi Arabia 0.510988815 0.007950555 0.345678780
## Senegal -0.737159777 1.395144404 -0.652755108
## Serbia 0.466010488 -1.022536304 -0.412148909
## Seychelles 0.319830923 -0.513898560 -0.118074665
## Sierra Leone -1.749172149 1.487623994 -0.685545205
## Singapore 1.365577041 -1.187678429 1.835145727
## Slovak Republic 0.555967143 -1.002719249 0.198368862
## Slovenia 1.005750419 -0.910239659 0.569371618
## Solomon Islands -0.995785161 0.853478234 -0.636932932
## South Africa -1.827884223 -0.236459790 -0.310123151
## South Korea 1.073217911 -1.134832949 0.498444620
## Spain 1.275620385 -1.042353359 0.967653988
## Sri Lanka 0.432276742 -0.494081505 -0.554002904
## St. Vincent and the Grenadines 0.117428448 -0.579955409 -0.367410341
## Sudan -0.478534393 1.276242074 -0.626566678
## Suriname -0.028751117 -0.282699585 -0.254472738
## Sweden 1.230642058 -0.639406574 2.135221486
## Switzerland 1.309354131 -0.943268084 3.362804135
## Tajikistan -0.107463190 0.371263230 -0.667049626
## Tanzania -1.265655127 1.639554749 -0.669013758
## Thailand 0.679657544 -0.923451029 -0.430153454
## Timor-Leste 0.061205539 2.168009548 -0.510901113
## Togo -1.333122619 1.269636389 -0.680689433
## Tonga -0.073729444 0.635490629 -0.513629075
## Tunisia 0.713391290 -0.533715615 -0.481439130
## Turkey 0.859570855 -0.527109930 -0.123530588
## Turkmenistan -0.298621083 -0.077923350 -0.465071361
## Uganda -1.546769675 2.115164068 -0.674851596
## Ukraine -0.017506535 -0.996113564 -0.545273427
## United Arab Emirates 0.668412962 -0.712069109 1.202258672
## United Kingdom 1.095707075 -0.679040684 1.415039665
## United States 0.915793764 -0.672434999 1.933352339
## Uruguay 0.657168380 -0.573349724 -0.058059514
## Uzbekistan -0.197419845 -0.401601915 -0.632022601
## Vanuatu -0.849605596 0.364657545 -0.545273427
## Venezuela 0.544722561 -0.315728010 0.029235252
## Vietnam 0.286097177 -0.659223629 -0.635841747
## Yemen -0.343599410 1.137522689 -0.635841747
## Zambia -2.086509607 1.619737694 -0.627657863NbClust(as.matrix(donnee), min.nc = 3, max.nc = 15, method = "ward.D")
## *** : The Hubert index is a graphical method of determining the number of clusters.
## In the plot of Hubert index, we seek a significant knee that corresponds to a
## significant increase of the value of the measure i.e the significant peak in Hubert
## index second differences plot.
## 
## *** : The D index is a graphical method of determining the number of clusters.
## In the plot of D index, we seek a significant knee (the significant peak in Dindex
## second differences plot) that corresponds to a significant increase of the value of
## the measure.
##
## *******************************************************************
## * Among all indices:
## * 4 proposed 3 as the best number of clusters
## * 9 proposed 4 as the best number of clusters
## * 1 proposed 5 as the best number of clusters
## * 1 proposed 8 as the best number of clusters
## * 5 proposed 9 as the best number of clusters
## * 1 proposed 12 as the best number of clusters
## * 1 proposed 14 as the best number of clusters
## * 1 proposed 15 as the best number of clusters
##
## ***** Conclusion *****
##
## * According to the majority rule, the best number of clusters is 4
##
##
## *******************************************************************## $All.index
## KL CH Hartigan CCC Scott Marriot TrCovW TraceW
## 3 1.8427 57.8307 20.9221 -2.4313 418.9626 5.164539e+16 17615.022 876.1166
## 4 1.5564 50.1387 14.8863 -2.6786 609.3518 2.936225e+16 13591.412 776.9927
## 5 1.1442 44.4853 12.5772 -3.1997 758.7814 1.875028e+16 12060.060 711.9705
## 6 0.2926 40.6143 28.1333 -3.4454 808.6017 2.003593e+16 9447.050 660.6776
## 7 2.0767 44.1722 16.2945 0.1436 962.9977 1.081897e+16 6363.185 562.4029
## 8 0.5419 43.7703 28.2797 1.4605 1070.1097 7.440776e+15 4995.833 510.4213
## 9 4.3721 48.3399 9.3875 5.1119 1220.3724 3.829616e+15 3394.298 433.3464
## 10 1.1997 46.2701 8.1650 5.2609 1293.2347 3.056237e+15 3031.433 409.0434
## 11 0.8340 44.3410 8.9717 5.3083 1376.7840 2.242316e+15 2823.262 388.8221
## 12 1.2044 43.1654 7.8186 5.6184 1447.0356 1.752186e+15 2505.380 367.6767
## 13 0.9742 41.9434 7.8612 5.7962 1506.8698 1.437148e+15 2361.741 350.0208
## 14 1.5395 41.0299 5.8597 6.0549 1560.7539 1.207096e+15 2068.108 333.0212
## 15 1.2204 39.7156 5.0920 6.0050 1614.6635 1.003397e+15 1975.666 320.7374
## Friedman Rubin Cindex DB Silhouette Duda Pseudot2 Beale Ratkowsky
## 3 25.3844 1.7053 0.2347 1.5929 0.2289 0.6755 15.3735 2.7975 0.3307
## 4 36.3323 1.9228 0.2246 1.4508 0.2470 0.8298 12.9207 1.2123 0.3286
## 5 40.4147 2.0984 0.2063 1.7295 0.2079 0.7280 24.6545 2.2097 0.3070
## 6 42.7143 2.2613 0.2032 1.7717 0.1599 0.3414 17.3592 10.4241 0.2951
## 7 51.2007 2.6565 0.1987 1.5066 0.1827 0.7968 10.4568 1.4951 0.2928
## 8 54.2108 2.9270 0.1882 1.4706 0.2036 1.0665 -1.6830 -0.3609 0.2832
## 9 56.8841 3.4476 0.3108 1.2326 0.2160 0.7129 10.4715 2.3289 0.2800
## 10 59.8853 3.6524 0.2997 1.2020 0.2206 0.7251 12.1343 2.2081 0.2688
## 11 62.3662 3.8424 0.2914 1.2141 0.2056 0.4977 12.1126 5.5951 0.2587
## 12 64.6251 4.0634 0.2862 1.1860 0.2105 0.6908 9.4000 2.5657 0.2503
## 13 68.3495 4.2683 0.2798 1.2286 0.1915 0.7334 11.6328 2.1168 0.2424
## 14 70.8060 4.4862 0.2721 1.2700 0.1875 0.7291 7.4314 2.1250 0.2353
## 15 72.5606 4.6580 0.2654 1.3223 0.1767 0.5385 13.7138 4.8442 0.2286
## Ball Ptbiserial Frey McClain Dunn Hubert SDindex Dindex SDbw
## 3 292.0389 0.4053 -0.1502 1.1448 0.0751 0.0014 2.8973 1.9790 0.9576
## 4 194.2482 0.4357 0.4909 1.1797 0.0757 0.0016 3.0800 1.8707 1.0002
## 5 142.3941 0.4312 5.5517 1.5461 0.0757 0.0019 3.1602 1.7666 0.9660
## 6 110.1129 0.3474 -0.1479 2.5747 0.0685 0.0019 3.1581 1.6756 0.7597
## 7 80.3433 0.3571 0.1256 2.5488 0.0685 0.0022 3.1016 1.5843 0.6454
## 8 63.8027 0.3659 -0.1291 2.8953 0.0717 0.0023 3.1233 1.5211 0.6410
## 9 48.1496 0.3835 0.1872 2.8069 0.1221 0.0025 2.9451 1.4625 0.4967
## 10 40.9043 0.3829 0.8481 2.9427 0.1221 0.0026 2.9247 1.4258 0.4672
## 11 35.3475 0.3608 0.0927 3.4443 0.1221 0.0026 3.1190 1.3866 0.4425
## 12 30.6397 0.3617 0.4867 3.4868 0.1221 0.0026 3.0365 1.3450 0.4064
## 13 26.9247 0.3521 1.0162 3.7714 0.1154 0.0027 2.9761 1.3048 0.3864
## 14 23.7872 0.3208 0.4286 4.6963 0.1154 0.0027 3.4028 1.2676 0.3676
## 15 21.3825 0.3095 1.4422 5.1586 0.1154 0.0028 3.4239 1.2396 0.3519
##
## $All.CriticalValues
## CritValue_Duda CritValue_PseudoT2 Fvalue_Beale
## 3 0.6825 14.8875 0.0037
## 4 0.7508 20.9124 0.2845
## 5 0.7548 21.4445 0.0200
## 6 0.4954 9.1671 0.0000
## 7 0.7098 16.7607 0.1478
## 8 0.6621 13.7821 1.0000
## 9 0.6573 13.5542 0.0158
## 10 0.6825 14.8875 0.0216
## 11 0.5447 10.0311 0.0000
## 12 0.6292 12.3746 0.0083
## 13 0.6825 14.8875 0.0282
## 14 0.6225 12.1297 0.0296
## 15 0.5901 11.1141 0.0000
##
## $Best.nc
## KL CH Hartigan CCC Scott Marriot TrCovW
## Number_clusters 9.0000 3.0000 9.0000 14.0000 4.0000 5.000000e+00 4.00
## Value_Index 4.3721 57.8307 18.8923 6.0549 190.3892 1.189761e+16 4023.61
## TraceW Friedman Rubin Cindex DB Silhouette Duda
## Number_clusters 9.0000 4.000 9.0000 8.0000 12.000 4.000 4.0000
## Value_Index 52.7719 10.948 -0.3158 0.1882 1.186 0.247 0.8298
## PseudoT2 Beale Ratkowsky Ball PtBiserial Frey McClain
## Number_clusters 4.0000 4.0000 3.0000 4.0000 4.0000 2 3.0000
## Value_Index 12.9207 1.2123 0.3307 97.7907 0.4357 NA 1.1448
## Dunn Hubert SDindex Dindex SDbw
## Number_clusters 9.0000 0 3.0000 0 15.0000
## Value_Index 0.1221 0 2.8973 0 0.3519
##
## $Best.partition
## Afghanistan Albania
## 1 2
## Algeria Angola
## 2 1
## Antigua and Barbuda Argentina
## 2 2
## Armenia Australia
## 2 3
## Austria Azerbaijan
## 3 2
## Bahamas Bahrain
## 2 4
## Bangladesh Barbados
## 1 2
## Belarus Belgium
## 2 3
## Belize Benin
## 2 1
## Bhutan Bolivia
## 1 1
## Bosnia and Herzegovina Botswana
## 2 1
## Brazil Brunei
## 2 4
## Bulgaria Burkina Faso
## 2 1
## Burundi Cambodia
## 1 1
## Cameroon Canada
## 1 3
## Cape Verde Central African Republic
## 2 1
## Chad Chile
## 1 2
## China Colombia
## 2 2
## Comoros Congo Dem. Rep.
## 1 1
## Congo Rep. Costa Rica
## 1 2
## Cote d'Ivoire Croatia
## 1 2
## Cyprus Czech Republic
## 2 2
## Denmark Dominican Republic
## 3 2
## Ecuador Egypt
## 2 1
## El Salvador Equatorial Guinea
## 2 1
## Eritrea Estonia
## 1 2
## Fiji Finland
## 1 3
## France Gabon
## 3 1
## Gambia Georgia
## 1 2
## Germany Ghana
## 3 1
## Greece Grenada
## 3 2
## Guatemala Guinea
## 2 1
## Guinea-Bissau Guyana
## 1 1
## Haiti Hungary
## 1 2
## Iceland India
## 3 1
## Indonesia Iran
## 2 2
## Iraq Ireland
## 1 3
## Israel Italy
## 3 3
## Jamaica Japan
## 2 3
## Jordan Kazakhstan
## 2 2
## Kenya Kiribati
## 1 1
## Kuwait Kyrgyz Republic
## 4 1
## Lao Latvia
## 1 2
## Lebanon Lesotho
## 2 1
## Liberia Libya
## 1 4
## Lithuania Luxembourg
## 2 4
## Macedonia FYR Madagascar
## 2 1
## Malawi Malaysia
## 1 2
## Maldives Mali
## 2 1
## Malta Mauritania
## 4 1
## Mauritius Micronesia Fed. Sts.
## 2 1
## Moldova Mongolia
## 2 2
## Montenegro Morocco
## 2 2
## Mozambique Myanmar
## 1 1
## Namibia Nepal
## 1 1
## Netherlands New Zealand
## 3 3
## Niger Nigeria
## 1 1
## Norway Oman
## 3 4
## Pakistan Panama
## 1 2
## Paraguay Peru
## 2 2
## Philippines Poland
## 1 2
## Portugal Qatar
## 3 4
## Romania Russia
## 2 2
## Rwanda Samoa
## 1 2
## Saudi Arabia Senegal
## 4 1
## Serbia Seychelles
## 2 2
## Sierra Leone Singapore
## 1 4
## Slovak Republic Slovenia
## 2 2
## Solomon Islands South Africa
## 1 1
## South Korea Spain
## 2 3
## Sri Lanka St. Vincent and the Grenadines
## 2 2
## Sudan Suriname
## 1 2
## Sweden Switzerland
## 3 3
## Tajikistan Tanzania
## 1 1
## Thailand Timor-Leste
## 2 1
## Togo Tonga
## 1 2
## Tunisia Turkey
## 2 2
## Turkmenistan Uganda
## 1 1
## Ukraine United Arab Emirates
## 2 4
## United Kingdom United States
## 3 3
## Uruguay Uzbekistan
## 2 1
## Vanuatu Venezuela
## 1 2
## Vietnam Yemen
## 2 1
## Zambia
## 1Nbclust Cutree
nbc <- 3
gpe.ward <- cutree(cah.ward, k = nbc) # Classe affectée pour chaque individu
gpe.min <- cutree(cah.min, k = nbc)
gpe.max <- cutree(cah.max, k = nbc)
plot(cah.ward, hang = -1, main = "Distance de Ward")
rect.hclust(cah.ward, nbc, border = "blue")
plot(cah.min, hang = -1, main = "Distance du saut minimal")
rect.hclust(cah.min, nbc, border = "blue")
plot(cah.max, hang = -1, main = "Distance du saut maximal")
rect.hclust(cah.max, nbc, border = "blue")
faire une clusplot
clusplot(donnee, gpe.ward, labels = nbc, col.p = as.numeric(gpe.ward))
Partie 3 : Agragation autour des centres mobiles
Classifiaction mixte Classifiaction finale
3 - Comparaison des résultats obtenus avec les différentes méthodes
Caract ́erisation de la partition obtenue Repr ́esentation informative des r ́esultats . Graphiques adapt ́es, repr ́esentations factorielles si adapt ́ees Optionnel : Repr ́esentation spatiale des r ́esultats sur la carte de Rennes Faire une ACP
4 - Conclusion vis à vis des choix effectués
Quels points peuvent ˆetre critiqu ́es dans vos choix Quelles pistes pourraient ˆetre explor ́ees pour aller plus loin et/ou mieux explorer ces donn ́ees ?